Link to actual problem [8912] \[ \boxed {y^{\prime }-F \left (y-x^{2}\right )=2 x} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
My program’s symgen result This shows my program’s found \(\xi ,\eta \) and the corresponding ODE in canonical coordinates \(R,S\).\begin{align*} \xi &= 1 \\ \eta &=2 x \\ \frac {dS}{dR} &= \frac {1}{F \left (R \right )} \\ \end{align*}